Solving a Strange Matrix Problem with Infinite Solutions

In summary, this equation represents the line in four-dimensional space that coincides with the w-axis.
  • #1
boa_co
11
0
Hi,

Homework Statement



I was given a linear equation system of the form Ax=b where x=(x, y, z, w),
I reduced (A|b) to its canonical form which is this:

Homework Equations



1_140250080.gif


The Attempt at a Solution



At first I thought that this means that there is an infinite number of solutions with one freedom degree.
But I cannot imagine in the world what the solution vector might look like.
I am sorry if this seems like a stupid question but can anyone please explain this to me?

Thanks
 

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  • #2
boa_co said:
Hi,

Homework Statement



I was given a linear equation system of the form Ax=b where x=(x, y, z, w),
I reduced (A|b) to its canonical form which is this:

Homework Equations



1_140250080.gif


The Attempt at a Solution



At first I thought that this means that there is an infinite number of solutions with one freedom degree.
But I cannot imagine in the world what the solution vector might look like.
I am sorry if this seems like a stupid question but can anyone please explain this to me?

Thanks

Just read them off your final augmented matrix: x = 0, y = 0, z = 0; w is arbitrary. The solution represents the line in four-dimensional space that coincides with the w-axis.
 
  • #3
Do you mean that if we assign w=t a general solution could be V=(0,0,0,t)?
 
  • #5
O.K Iunderstand the technical side of what you are saying Av=0, but the equation you get is 0w=0. How can this have any meaning?
 
  • #6
Of course the equation 0w = 0 has meaning. It's true for any value of w.

The matrix equation you were working on was Ax = 0, so what you were finding was the nullspace of matrix A. The nullspace of A (or null(A)) maps all vectors of the form <0, 0, 0, t>T to the zero vector in R4.
 
  • #7
Got it now, thanks!
 

1. What is a strange matrix problem?

A strange matrix problem is a mathematical problem that involves manipulating a matrix using specific operations or algorithms to solve a given question or puzzle. These problems often require critical thinking and creative problem-solving skills.

2. What are some examples of strange matrix problems?

Some examples of strange matrix problems include finding the determinant of a matrix, solving a system of linear equations using matrix operations, and determining the inverse of a matrix.

3. How do you approach solving a strange matrix problem?

The first step in solving a strange matrix problem is to understand the given problem and identify the key operations or algorithms needed to solve it. Then, carefully apply these operations to the matrix, making sure to follow the correct order of operations. Finally, double-check your solution and make any necessary adjustments.

4. What are the benefits of solving strange matrix problems?

Solving strange matrix problems can improve critical thinking skills, mathematical reasoning skills, and creativity. It can also help develop problem-solving strategies that can be applied to other areas of science and mathematics.

5. Are there any real-world applications of strange matrix problems?

Yes, strange matrix problems have many real-world applications, such as in computer graphics, cryptography, and data analysis. They are also used in various fields of science, including physics, engineering, and economics, to model and solve complex systems.

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